Conventionally, in flow channels of an impeller in a centrifugal or a mixed flow turbomachinery, main flows flowing along the flow channels are affected by secondary flows generated by movement of low energy fluid in boundary layers on wall surfaces due to static pressure gradients in the flow channels. This phenomenon leads to the formation of streamwise vortices or flows having non-uniform velocity in the flow channel, which in turn results in a substantial fluid energy loss not only in the impeller but also in the diffuser or guide vanes downstream of the impeller.
The secondary flow is defined as a flow which has a velocity component perpendicular to the main flow. The total energy loss caused by the secondary flows is referred to as the secondary flow loss. The low energy fluid accumulated at a certain region in the flow channel may cause flow separation on a large scale, thus producing a positively sloped characteristic curve and hence preventing stable operation of the turbomachine.
There is a known approach for suppressing the secondary flows in a turbomachine which is to make the impeller have a specific flow channel geometry. As an example of such approach using a specific flow channel geometry, there is a known method in which blades of the impeller in an axial turbomachine are leaned towards the circumferential direction thereof or the direction of the suction or the discharge side (L. H. Smith and H. Yeh, "Sweep and Dihedral Effects in Axial Flow Turbomachinery", Trans ASME, Journal of Basic Engineering, Vol. 85, No. 3, 1963, pp. 401-416), or a method in which blades in a turbine cascade are leaned or curved toward a circumferential direction thereof (W. Zhongqi, et al., "An Experimental Investigation into the Reasons of Reducing Secondary Flow Losses by Using Leaned Blades in Rectangular Turbine Cascades with Incidence Angle", ASME Paper 88-GT-4), or a method in which a radial rotor has a blade curvature in the spanwise direction with a convex blade pressure surface and/or a concave blade suction surface (GB2224083A). These methods are known to have a favorable influence upon the secondary flows in the flow channel if applied appropriately.
However, since the influence of the profile of a blade camber line or a blade cross-section upon the secondary flow has not been essentially known, the effect of blade lean or spanwise blade curvature is utilized under a certain limitation without changing the blade camber line or the blade cross-section substantially. Further, Japanese laid-open Patent Publication No. 60-10281 discloses a structure in which a projecting portion is provided at the corner of a hub surface and a blade surface in a turbomachine to reduce the secondary flow loss. Since such flow channel profile is a specific blade profile having a nonaxisymmetric hub surface, it is difficult to manufacture the impeller.
In all cases of the above prior art, the method of achieving the effect universally has not been sufficiently studied. Therefore, the universal methods of suppressing the secondary flows under different design conditions and for different types of turbomachines have not been established. Under these circumstances, there are many cases that the above effect is reduced, or to make matters worse, undesirable effects are obtained.
In general, the three-dimensional geometry of an impeller is defined as a meridional geometry formed by a hub surface and a shroud surface and a blade profile serving to transmit energy to fluid. As the meridional geometry, various geometries including a centrifugal type, a mixed flow type and an axial flow type are selected in accordance with design specifications, including flow rate, pressure head and rotational speed, which are required in the individual turbomachinery. As a type number characterizing the meridional geometry of an impeller, a specific speed N.sub.s =NQ.sup.1/2 /H.sup.3/4 (for pumps), is widely used for designing of the impeller. Here, N is the rotational speed in revolutions per minute (rpm), Q is the flow rate in cubic meters per minute (m.sup.3 /min) and H is the head in meters (m) representing fluid energy which is imparted to the fluid by the turbomachinery. That is, the specific speed is determined if the design specifications are given, and the meridional geometry of the impeller can be suitably selected in accordance with the specific speed. Incidentally, Q is defined as volume flow rate, and in case of a compressor or the like, the volume flow rate at an impeller inlet is used for a compressible fluid whose volume is variable between the impeller inlet and the impeller exit.
With regard to a blade profile, the inlet blade angle is determined by the assumed inlet velocity triangle at each spanwise location to match the inlet blade angle with the inlet flow angle. On the other hand, the exit blade angle is determined by the assumed exit velocity triangle at each spanwise location to satisfy the design head. The inlet and the exit velocity triangles are calculated from the meridional geometry and the design flow rate and the design head, but can be updated based on the results of flow calculations of the impeller. However, there are many degrees of freedom as to ways of determining blade angle distribution which controls inlet and exit blade angles, and in effect the choice of the blade angle distribution is left to designer's intuition.
There have been proposed up to now many methods in accordance with the approach which makes the impeller have a specific flow channel geometry to suppress the secondary flows. However, since the method of achieving the effect universally has not been sufficiently studied, design criterion of blade profiles having many degrees of freedom has not been established. Therefore, universal methods of suppressing the secondary flows under different design conditions and for different specific speeds have not been established. Under these circumstances, the three-dimensional geometry of the impeller has been designed on the basis of variation of blade angle distribution of the impeller by trial and error to find the optimum profile of the impeller for suppressing the secondary flow.
Next, a conventional method of designing the three-dimensional geometry of the impeller on the basis of variation of blade angle distribution by trial and error will be described below in accordance with a flow chart in FIG. 3(A).
In the first step (step of determining meridional plane), the design specification is input to determine the meridional geometry and the number of blades of the impeller. Next, a plurality of surfaces of revolution are defined on a meridional flow passage, and the tangential coordinate f.sub.0 of a blade camber line at a point on each of surface of revolution is specified based on past experience. The location, where the tangential coordinate f.sub.0 is specified, is selected at the leading edge or at the trailing edge of the impeller in many cases. Thus a specified location of the tangential coordinate f.sub.0 is referred as the stacking condition.
In the second step (step of determining blade angle distribution), the blade angle at the impeller inlet is determined from the meridional geometry of the impeller obtained by the first step and design flow rate. Next, the blade angle at the impeller exit is determined from the meridional geometry of the impeller obtained by the first step, and design head. A curve which connects smoothly the determined blade angle at the impeller inlet and the blade angle at the impeller exit is defined to determine the blade angle distribution along the location of non-dimensional meridional distance m.
In the third step (step of determining a blade profile), tangential coordinate (wrap angle) of the blade camber line in each of the locations of non-dimensional meridional distance m is determined by integrating .differential.f/.differential.m=1/(r tan .beta.) with the location of non-dimensional meridional distance m on the basis of blade angle distribution .beta. between the impeller inlet and the impeller exit along each stream line in the location of non-dimensional meridional distance m, using stacking condition f.sub.0 as an initial value. The three-dimensional geometry of the impeller is determined by adding a certain thickness to the determined blade camber line to allow the blade to have mechanical strength.
In the fourth step (step of evaluating flow fields), three-dimensional inviscid flow analysis which is a flow analysis without consideration of viscosity of fluid is applied to the three-dimensional geometry of the impeller determined by the third step, and a possibility of poor performance caused by flow separation due to rapid deceleration of flow in the impeller is evaluated. In the case where it is judged that the pressure distribution in the impeller is not appropriate, after going back to the second step to modify the blade angle distribution, the steps from the second step to the fourth step are repeated until the expected result is achieved.
In case of suppressing the secondary flow by the above-mentioned conventional method of manufacturing the impeller, the following disadvantages are enumerated.
(1) In the fourth step, the criteria (including the dependence on the specific speed of the impeller) for judging whether optimum pressure distribution in the flow channel is achieved to suppress the secondary flow is uncertain. Though the state of generation of the secondary flows can be examined by three-dimensional viscous flow analysis, an enormous amount of calculations is required, thus optimization of the blade profile of the impeller by repeating the steps from the second step to the fourth step is practically not infeasible.
(2) Although it is necessary to make the blade angle distribution proper in the second step, if the blade angle distribution which achieves the secondary flow suppression deviates greatly from conventional experience, it is difficult to assume favorable blade angle distribution. Therefore, in practice, it has been difficult to find by trial and error the optimum blade profile of the impeller for suppressing secondary flow.
However, recently, as a design method of a blade profile of the impeller, it is known that if a blade loading distribution is given, the three-dimensional geometry of the impeller which realizes the given blade loading distribution can be determined by using a three-dimensional inverse design method which is published in the following literature.
Zangeneh, M., 1991, "A Compressible Three Dimensional Blade Design Method for Radial and Mixed Flow Turbomachinery Blades", International Journal of Numerical Methods in Fluids, Vol. 13, pp. 599-624., Borges, J. E., 1990, "A Three-Dimensional Inverse Method for Turbomachinery: Part I--Theory", Transaction of the ASME, Journal of Turbomachinery, Vol. 112, pp. 346-354, Yang, Y. L., Tan, C. S. and Hawthorne, W. R., 1992, "Aerodynamic Design of Turbomachinery Blading in Three-Dimensional Flow: An Application to Radial Inflow Turbines", ASME Paper 92-GT-74, Dang, T. Q., 1993, "A Fully Three-Dimensional Inverse Method for Turbomachinery Blading in Transonic Flows", Transactions of the ASME, Journal of Turbomachinery, Vol. 115, pp. 354-361, Borges, J. E., 1993 "A proposed Through-Flow Inverse Method for the Design of Mixed-Flow Pumps", International Journal for Numerical Methods in Fluids, Vol. 17, pp. 1097-1114.
Most of the above methods design the blade shape based on the three-dimensional inviscid flow through the blade channels. However, the method described by Borges (1993) uses a more approximate Actuator Duct approach in which the flow field is assumed to be axisymmetric. Such an approximate approach can provide a very computationally efficient means of arriving at the blade geometry for a specified loading distribution. However, the errors in this approach become quite high for very highly loaded turbomachines such as centrifugal pumps. Incidentally, in none of these literatures has the inverse design method been used for the purpose of suppression of secondary flows in an impeller.
It is apparent from the secondary flow theory that the secondary flow in the impeller results from the action of the Coriolis force caused by the rotation of the impeller and the effects of the streamline curvature. The secondary flow in the impeller is divided broadly into two categories, one of which is blade-to-blade secondary flow generated along a shroud surface or a hub surface, the other of which is the meridional component of secondary flow generated along the pressure surface or the suction surface of a blade.
It is known that the blade-to-blade secondary flow can be minimized by making the blade profile to be backswept. Regarding the other type of secondary flow, that is, the meridional component of secondary flow, it is difficult to weaken or eliminate it easily. If we wish to weaken or eliminate the meridional component of secondary flow, it is necessary to optimize the three-dimensional geometry of the flow channel very carefully.
The purpose of the present invention is to suppress the meridional component of secondary flow in a centrifugal or a mixed flow turbomachine.
As an example of a typical impeller in the turbomachinery to which the present invention is applied, the three-dimensional geometry of a closed type impeller is schematically shown in FIGS. 1(A) and 1(B) in such a state that most of a shroud surface is removed. FIG. 1(A) is a perspective view partly in section, and FIG. 1(B) is a cross-sectional view taken along a line A-A' which is a meridional cross-sectional view. In FIGS. 1(A) and 1(B), a hub surface 2 extends radially outwardly from a rotating shaft 1 so that it has a curved surface similar to a corn surface. A plurality of blades 3 are provided on the hub surface 2 so that they extend radially outward from the rotating shaft 1 and are disposed at equal intervals in the circumferential direction. The blade tips 3a of the blades 3 are covered with a shroud surface 4 as shown in FIG. 1(B). A flow channel is defined by two blades 3 in confrontation with each other, the hub surface 2 and the shroud surface 4 so that fluid flows from an impeller inlet 6a toward an impeller exit 6b. When the impeller 6 is rotated about an axis of the rotating shaft 1 at an angular velocity .omega., fluid flowing into the flow channel form the impeller inlet 6a is delivered toward the impeller exit 6b of the impeller 6. In this case, the surface facing the rotational direction is the pressure surface 3b, and the opposite side of the pressure surface 3b is the suction surface 3c. In the case of open type impeller, there is no independent part for forming the shroud surface 4, but a casing (not shown in the drawing) for enclosing the impeller 6 serves as the shroud surface 4. Therefore, there is no basic fluid dynamical difference between the open type impeller and the closed type impeller in terms of the generation and the suppression of the meridional component of secondary flows, thus only the closed type impeller will be described below.
The impeller 6 having a plurality of blades 3 is incorporated as a main component, the rotating shaft 1 is coupled to a driving source, thereby jointly constituting a turbomachine. Fluid is introduced into the impeller inlet 6a through a suction pipe, pumped by the impeller 6 and discharged from the impeller exit 6b, and then delivered through a discharge pipe to the outside of the turbomachine.
The unsolved serious problem in connection with the impeller of a turbomachine is the suppression of the meridional component of secondary flow. The mechanism of generation of the meridional component of secondary flow, whose suppression is the purpose of this invention, is explained as follows:
As shown in FIG. 1(B), with regard to the relative flow, the reduced static pressure distribution, defined as p.sup.* =p-0.5.rho.u.sup.2, is formed by the action of a centrifugal force W.sup.2 /R due to streamline curvature of the main flow and the action of Coriolis force 2.omega.W.sub..theta. due to the rotation of the impeller, where W is the relative velocity of flow, R is the radius of streamline curvature, .omega. is the angular velocity of the impeller, W.sub..theta. is the component in the circumferential direction of W relative to the rotating shaft 1, p.sup.* is reduced static pressure, p is static pressure, .rho. is density of fluid, us is peripheral velocity at a certain radius r from the rotating shaft 1. The reduced static pressure p.sup.* has such a distribution in which the pressure is high at the hub side and low at the shroud side, so that the pressure gradient balances the centrifugal force W.sup.2 /R and the Coriolis force 2.omega.W.sub..theta. directed toward the hub side.
In the boundary layer along the blade surface, since the relative velocity W is reduced in the boundary layer developing along the wall surface, the centrifugal force W.sup.2 /R and the Coriolis force 2.omega.W.sub..theta. acting on the fluid in the boundary layer become small. As a result, they cannot balance the reduced static pressure gradient of the main flow, and low energy fluid in the boundary layer flows towards an area of low reduced static pressure p.sup.*, thus generating the meridional component of secondary flow. That is, as shown in broken lines on the pressure surface 3b and in solid lines on the suction surface 3c in FIG. 1(A), fluid moves along the blade surface from the hub side towards the shroud side on the pressure surface 3b and the suction surface 3c forming meridional component of secondary flow.
The meridional component of secondary flow is generated on both surfaces of the suction surface 3c and the pressure surface 3b. In general, since the boundary layer on the suction surface 3c is thicker than that on the pressure surface 3b, the secondary flow on the suction surface 3c has a greater influence on performance characteristics of turbomachinery. The purpose of the present invention is to suppress the meridional component of secondary flow in the suction surface of the blade.
When low energy fluid in the boundary layer moves from the hub side to the shroud side, fluid flow is formed from the shroud side to the hub side at around the midpoint location to compensate for fluid flow rate which has moved. As a result, as shown schematically in FIG. 2(B) which is a cross-sectional view taken along a line B-B' in FIG. 2(A), a pair of vortices which have a different swirl direction from each other are formed in the flow channel between two blades as the flow goes towards exit. These vortices are referred to as secondary vortices. Low energy fluid in the flow channel is accumulated due to these vortices at a certain location of the impeller towards the exit where the reduced static pressure p.sup.* is lowest, and this low energy fluid is mixed with fluid which flows steadily in the flow channel, resulting in generation of a great flow loss.
Furthermore, when the non-uniform flow generated by insufficient mixing of a low relative velocity (high loss) fluid and a high relative velocity (high loss) fluid is discharged to the downstream flow channel of the blades, a great flow loss is generated when both fluids are mixed.
Such a non-uniform flow leaving the impeller makes the velocity triangle unfavorable at the inlet of the diffuser and causes flow separation on diffuser vanes or a reverse flow within a vaneless diffuser, resulting in a substantial decrease of the overall performance of the turbomachine.
Furthermore, in the area of high loss fluid accumulated at a certain location in the flow channel, a large scale reverse flow is liable to occur, thus producing a positively sloped characteristics curve. As a result, surging, vibration, noise and the like are generated, and the turbomachinery cannot be stably operated especially at partial flow rate.
Therefore, in order to improve the performance of centrifugal or mixed flow turbomachinery and realize stable operation of turbomachinery, it is necessary to design the three-dimensional geometry of the flow channel for suppressing the secondary flow as much as possible, whereby the formation of secondary vortices, the resulting non-uniform flow, and large scale flow separation or the like may be prevented.